|
|
A099448
|
|
A Chebyshev transform of A030191 associated to the knot 7_6.
|
|
1
|
|
|
1, 5, 19, 65, 216, 715, 2369, 7855, 26051, 86400, 286549, 950345, 3151831, 10453085, 34667784, 114976135, 381319781, 1264651795, 4194233399, 13910227200, 46133441401, 153002131805, 507433471819, 1682909416265, 5581389996216
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The denominator is a parameterization of the Alexander polynomial for the knot 7_6. The g.f. is the image of the g.f. of A030191 under the Chebyshev transform A(x)->(1/(1+x^2))A(x/(1+x^2)).
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1+x^2)/(1-5x+7x^2-5x^3+x^4); a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*sum{j=0..n-2k, C(n-2k-j, j)(-5)^j*5^(n-2k-2j)}}; a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*A030191(n-2k)); a(n)=sum{k=0..n, binomial((n+k)/2, k)(-1)^((n-k)/2)(1+(-1)^(n+k))A030191(k)/2}; a(n)=sum{k=0..n, A099449(n-k)*binomial(1, k/2)(1+(-1)^k)/2};
|
|
MATHEMATICA
|
CoefficientList[Series[(1+x^2)/(1-5x+7x^2-5x^3+x^4), {x, 0, 30}], x] (* or *)
LinearRecurrence[{5, -7, 5, -1}, {1, 5, 19, 65}, 30] (* Harvey P. Dale, Nov 27 2013 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|